2
votes
1answer
79 views

Why we use $\mathbb{R}^{m \times n}$ notation instead of $\mathbb{R}^{n \times m}$?

I just realised, that I use all the time the notation $\mathbb{R}^{n \times m}$, and all books and papers use $\mathbb{R}^{m \times n}$. $\mathbb{R}^{n \times m}$ is more sympathetic for me, because I ...
0
votes
0answers
11 views

Notation for concatenation of indexed vectors/matrices

Is there any standard notation for concatenation of matrices/vectors where their indices are taken from a set. I have matrices $A_{ij}$ where $(i,j)\in S$. I want to denote a matrix $A$ which is the ...
0
votes
1answer
23 views

What's the correct notation for a minimum of a row of a matrix?

Let I=1,...,m denote the indexes of the rows of a matrix A Let J=1,...,n denote the indexes of the columns of a matrix A Let xi,j denote the value of the element A[i,j] I need do use a notation to ...
3
votes
2answers
130 views

What is the intutive explanation of why the notation of matrices is as it is?

If I want to solve a system of linear equations, like 2x-y=1 x+2y=4 Then the matrix notation for the same would be: $$ \begin{bmatrix} 2 & -1 \\ 1 & 2 \\ \end{bmatrix} \begin{bmatrix} X\\ ...
1
vote
2answers
97 views

Matrix-Multiplication

I have to matrices: $$A=\pmatrix{1&a&1\\1&0&a\\1&2&0} ; \quad B= \pmatrix{1&b&3\\2&1&0}$$ The task is to determine $AB, AB^T, BA$ I think i cannot ...
0
votes
1answer
31 views

Notation for matrix and sum of matrix rows

I have a table that describes the influence of sources (columns) on sinks (rows) where rows=$(A,B,C)$ and columns=$(A,B,C,D,E)$. So my table looks like: ...
1
vote
0answers
22 views

element subset for adjacency matrix

I am trying to create an element of a matrix that is a subset of a larger matrix. However, I am told that my subscripts do not match. I wanted other people's opinion as to what I am doing wrong and ...
0
votes
1answer
23 views

Basic matrice notation

I want to compute the L2 distance between a set of points X and M using matrices, for that I proceed as follows: 1) I substract both matrices, X-M 2) I square each matrice member (X-M)^2 3) I ...
0
votes
0answers
23 views

Column or row of a matrix?

The question is so simple, but I cannot find the answer. Is $M_i$ (usually) the $i^{\text{th}}$ column of matrix $M$? Or the $i^{\text{th}}$ row? Since $M_{ij}$ is the $j^{\text{th}}$ element of the ...
1
vote
1answer
38 views

$\mathbb{R}_*$ Notation

What does the notation $\mathbb{R}_*$ denote? I am seeing it used for showing domain of matrices, $M\in \mathbb{R}_*^{a \times b}$, which is different from $N \in \mathbb{R}^{a \times b}$. But I do ...
0
votes
0answers
54 views

Notation in Linear Algebra

What does $(A\mid b)$ denote in Linear Algebra? Specifically in the context of the following question: "If $(A\mid b)$ is in reduced row echelon form, prove that A is also in reduced row echelon ...
3
votes
1answer
50 views

Is there a way in matrix math notation to show the 'flip up-down', and 'flip left-right' of a matrix?

Title says it all - is there an accepted mathematical way in matrix notation to show those operations on a matrix? Thanks.
1
vote
0answers
36 views

problems on define set with polynomials

I'm trying to say set A is the set of nonnegative integers that not of this two forms $3x^2 + (6y-4)x - y\ $ and $\ 3x^2 + (6y-2)x + (y - 1)$, for example: $4=3 \cdot1^2+(6 \cdot1-4) \cdot 1-1\ $ is ...
1
vote
0answers
22 views

Notation for appending 2 submatrices

I have a matrix $M$ with $i$ rows and $(e+n)$ columns: $M_{i,e+n}$ I would like to express that $M_{i,e+n}$ is the result of appending $M_{i,e}$ and $M_{i,n}$ What is the algebraic notation to ...
0
votes
0answers
9 views

Question about notation matrix of partial derivatives where one component has two indices

lets suppose we have a vector ($\delta_{11}, \delta_{12}, \dots, \delta_{jk}$) where $\delta_{jk} = \alpha_j + \beta_k$, i.e., each element is build up of two components. The first index $j$ specifies ...
1
vote
2answers
30 views

Looking for notation of set of all entries of some matrix?

I'm busy writing my thesis, and I'm looking for some concise notation to denote the supremum of the matrix entries of, say $A \in M_n(\mathbb{R})$. How should I do this? Looking for something like ...
3
votes
2answers
48 views

Notation - Transpose of Block Matrices [Lay P121 Q2.4.12]

Definition of Transpose is $(A^T)_{ij} = A_{ji}$ $1.$ Why $\begin{bmatrix} M & N \end{bmatrix}^T = \begin{bmatrix} M^T \\ N^T \end{bmatrix}$, and NOT $\begin{bmatrix} M \\ N\end{bmatrix}$? ...
2
votes
4answers
400 views

Matrix Mathematical Notation

I am trying to work out the mathematical notation for combining the columns of two matrices, $$A=\begin{pmatrix}1 & 3 & 5 \\ 2 & 4 & 1 \\ 3 & 7 & 9\end{pmatrix}$$ and ...
0
votes
0answers
54 views

What is the Δ above the = symbol?

I am reading this and at equation 4.21 it has an equal symbol with a Δ above it. Do you know how this is called, and what it does? Thanks
0
votes
1answer
34 views

How to define a set for a matrix

I have a big matrix and I have partitioned it. So, I want to say that I am taking the summation of entries that do not belong to the blocks in the diagonal. How can I say it mathematically. Is it ...
1
vote
2answers
60 views

What is this form of 'notation' called?

I was reading some of Max Tegmark's lecture materials and I found this little thing. Is there a name for it? Specifically, I am talking about $S_1$ R $S_2$ & $S_1$ R $S_2$ and the matrix. Is ...
0
votes
0answers
27 views

A question regarding notation of equation

I'm reading a research paper, and, have come across this summation equation $$ S_{2} = \sum_{N -1}^{j = 0}w_{j}^{2}\cdot $$ My question is: if j = 0..... N-1 do I ...
1
vote
2answers
162 views

Notation for summing all elements under the diagonal of a square matrix

I have a simple question: What is the notation for summing all elements under the diagonal of a square matrix? I appreciate your help.
0
votes
0answers
76 views

Notation for Kronecker product of a matrix and itself?

What is the notation for the Kronecker product of a matrix and itself? In other words, is there a short-hand way I can express the following: $X⊗X$ $X⊗X⊗X$ $X⊗X⊗X⊗X$ Where $X$ is a matrix? What ...
2
votes
3answers
187 views

Basic question: what does the notation $[A,B]$ mean?

If $A$ and $B$ are both matrices, what is $[A,B]$? I understand that it is a commutator and that $[A,B]=AB-BA$, but since I don't know what a commutator is, none of this information is telling me ...
0
votes
1answer
57 views

Aggregating a vector of $1\times K$ into a vector $1\times J$, such as $J<K$

I am stuck with a matrix algebra operation: how do I do (and mainly which notation to use) to aggregate the numbers of a vector $1\times K$ into a vector of $1\times J$, such as $J$ is of course lower ...
2
votes
1answer
131 views

Notation for the set of symmetric matrices and symmetric positive definite matrices

I would like to know if there exists a notation for the set of symmetric matrices and symmetric positive definite matrices. For instance, the set of $N \times N$ matrices with real entries is denoted ...
0
votes
0answers
43 views

Alternate convention in matrix multiplication?

I'm going through Halmos's Finite-Dimensional Vectorspaces. I noticed an oddity in a proof where the indexes seemed to be swapped when multiplying a matrix by a vector. I went back about 30 pages to ...
1
vote
0answers
254 views

What is the modern use of $\bigodot$ sign?

I've seen $\bigodot$ used in various contexts. It's used for a special set theory operation by some authors (say, Saks) and as sign for Hadamard product by a couple other authors (say, Wiener) in the ...
2
votes
1answer
64 views

Matrix notation: Does empty space means a bunch of zeros?

I don't understand what is meant with the following notation: I think this means that the first row = 4 2 0 ... 0 second row = 1 4 1 0 ... 0 third row = 0 1 4 1 0 .. 0 etc. Is this correct ?
0
votes
1answer
53 views

What does the notation $H\biguplus RH$ mean?

I have some problems understanding the notation used in this question. Let $K:= \left\{P\in GL_{2}\mathbb{(R)}: P^{T}P=I_{2}\right\}, H:=\left\{A_{\theta}=\begin{pmatrix} \cos(\theta) & ...
0
votes
1answer
108 views

Clarification on matrix notation subscript and superscript notation

If a matrix C exists in integers $\mathcal{Z}_q^{mxl}$ what does this mean?
0
votes
2answers
34 views

What is the term to make one matrix from two or more?

I am looking for the proper term for the operation of creating one block matrix from two or more for example $[AB]$ from $A$, $B$. And what is the correct notation to denote such a matrix. Do we use a ...
1
vote
1answer
143 views

How to express this in matrix notation (row-wise normalisation)

My questions are: How do I describe the row sum of a matrix? How do I describe the number of non-zero elements per row of a matrix in matrix notation? How do I divide a vector elementwise? To give ...
1
vote
2answers
107 views

Matrix (correct) notation

Say I have a real $m \times n$ matrix $\mathbf{M}$. Shall I write $\mathbf{M} \in \mathbb{R}^{m \times n}$ or $\mathbf{M} \in \mathbb{R}^{m,n}$? What is commonly accepted and most beautiful and ...
2
votes
2answers
658 views

Bar symbol over a matrix

So I am reading a paper (not online) and I come across a definition: $$\mathbb E=R\bar R$$ Where R is a complex matrix. I am thinking that it means complex conjugate, but I honestly have never seen ...
2
votes
1answer
319 views

How to denote matrix concatenation?

Trivial question: Is there any standard notation for the concatenation of two or more matrices? Example: $$A = \left(\begin{array}[c c] - a_1 & a_2\\ a_3 & a_4 \end{array}\right),$$ $$B = ...
7
votes
2answers
135 views

Unsure about a maths symbol

Help, help, help! I've come across this maths symbol, $[n(i,j)]^{0.5}$ where $n$ is a square matrix. Does this mean that it is the $(i,j)$ element of $n^{0.5}$? or $n(i,j)^{0.5}$? source: ...
3
votes
1answer
237 views

What does the following symbol mean? (direct sum? o-plus? — subject: matrix theory)

In this paper equation 11, the author uses a symbol that is a cross in a circle. I believe I have seen that referred to as a direct sum, but I am not completely sure what that is. $$\bigoplus$$ ...
0
votes
1answer
164 views

What is this notation relating to the Jacobian matrix operation?

In the below image, in the very bottom-most equation is the partial differential at the end of the equation being multiplied to every element in the inverse Jacobian matrix (and then beta_n added)? Or ...
1
vote
1answer
125 views

What does this notation mean? Set of real numbers transposed??

In the below: from top of Page 13: http://www.ntuzov.com/Nik_Site/Niks_files/Research/papers/stat_arb/Ahmed_2009.pdf how do you interpret what x is an element of? It looks like the set of real ...
1
vote
2answers
101 views

Representing $m\times n$ matrix using ordered $n$-tuples and an $m$-tuple

Can a matrix, generally \begin{bmatrix} a_{1,1} &\cdots &a_{1,n} \\ \vdots &\ddots & \vdots \\ a_{m,1} &\cdots &a_{m,n} \end{bmatrix} be represented using ordered ...
2
votes
2answers
108 views

Ambiguous notation for squared matrix

What does $A^{2}$ mean for square $A$? Is it $AA$ or $AA^{T}$? Sometimes, the result may differ. Or there is no uniform approach?
2
votes
1answer
420 views

Is there a symbol for matrix multiplication operator?

Title says it all. Is there any specific operator symbol for matrix multiplication? Not just write down side by side but symbols like cross ($\times$).
3
votes
3answers
516 views

What is the notation for the set of all $m\times n$ matrices?

Given that $\mathbb{R}^n$ is the notation used for n-dimensional vectors, is there an accepted equivalent notation for matrices?
4
votes
2answers
213 views

$^t$, $^\dagger$, $^*$, $^H$, $^⊤$, and $^T$ : Which is which, and what do each mean?

I think this question's answer(s) will be of profound use to the future generation of human beings who happen to stumble upon the website math.stackexchange.com. What are the differences between ...
1
vote
0answers
72 views

Simplified matrix notation

There is a mathematical notation to define an array that you can write using standard keyboard characters on one line? for example:   1 3 8 7 10 17 22 6   5 10 23 8 11 98 7 12
5
votes
1answer
75 views

Is there a name for this given type of matrix?

Given a finite set of symbols, say $\Omega=\{1,\ldots,n\}$, is there a name for an $n\times m$ matrix $A$ such that every column of $A$ contains each elements of $\Omega$? (The motivation for this ...
0
votes
1answer
104 views

Notation minimum of a column vector

I'd like to know the notation to express the minimum of a column vector. Is this notation correct? \begin{equation} \min \left[\matrix{ \left|b_{n}-b_{n+1}\right| \cr ...
4
votes
6answers
99 views

$(\mathbf{u}^T\mathbf{v})\mathbf{v} = \mathbf{u}^T(\mathbf{v}\mathbf{v})$ doesn't hold for $\mathbf{u}, \mathbf{v}\in\mathbb{R}^n$ - why?

Suppose I have vectors $\mathbf{u}$ and $\mathbf{v}$ in $\mathbb{R}^n$. It is well defined to write $5\mathbf{v}$ or $c\mathbf{v}$ for scalar $c$. Since the inner product of $\mathbf{u}$ and ...